Potential artifacts in conservation laws and invariants inferred from sequential state estimation

Abstract. In sequential estimation methods often used in oceanic and general climate calculations of the state forecasts, observations act mathematically statistically as source or sink terms conservation equations for heat, salt, mass, momentum. These artificial obscure inference system's variability secular changes. Furthermore, purposes calculating changes important functions variables such total mass energy volumetric current transports, results both filter smoother-based estimates are sensitive to misrepresentation a large variety parameters, including initial conditions, prior uncertainty covariances, systematic random errors observations. Here, toy models coupled mass–spring oscillator system barotropic Rossby wave demonstrate many issues that arise from misrepresentations. Results Kalman those finite interval smoothing analyzed. (and prediction) problem, entry data leads violation other invariant rules. A method restores rules, but uncertainties all remain. Convincing trend time-dependent determinations “reanalysis-like” require full understanding models, observations, underlying error structures. Application smoother-type designed optimal reconstruction alleviate some issues.